ࡱ> /1.` bjbj ;J1 R       , ,,,8L,d,t, b0-(0(P0P0P0l2l2l2-b/b/b/b/b/b/b$chfSb l2h2l2l2l2Sb  P0P0hbz7z7z7l2j P0 P0-bz7l2-bz7z7qZ` J ^P0$- bK,2\8qa~b0b ]|g38gp^g ^l2l2z7l2l2l2l2l2SbSb6fl2l2l2bl2l2l2l2, , , 0%, , , 0%, , ,         Chapter 03.01 Solution of Quadratic Equations After reading this chapter, you should be able to: find the solutions of quadratic equations, derive the formula for the solution of quadratic equations, solve simple physical problems involving quadratic equations. What are quadratic equations and how do we solve them? A quadratic equation has the form  EMBED Equation.3 , where  EMBED Equation.3  The solution to the above quadratic equation is given by  EMBED Equation.3  So the equation has two roots, and depending on the value of the discriminant,  EMBED Equation.3 , the equation may have real, complex or repeated roots. If  EMBED Equation.3 , the roots are complex. If  EMBED Equation.3 , the roots are real. If  EMBED Equation.3 , the roots are real and repeated. Example 1 Derive the solution to  EMBED Equation.3 . Solution  EMBED Equation.3  Dividing both sides by  EMBED Equation.3 ,  EMBED Equation.3 , we get  EMBED Equation.3  Note if  EMBED Equation.3 , the solution to  EMBED Equation.3  is  EMBED Equation.3  Rewrite  EMBED Equation.3  as  EMBED Equation.3   EMBED Equation.3   EMBED Equation.3   EMBED Equation.3   EMBED Equation.3   EMBED Equation.3   EMBED Equation.3  Example 2 A ball is thrown down at 50 mph from the top of a building. The building is 420 feet tall. Derive the equation that would let you find the time the ball takes to reach the ground. Solution The distance  EMBED Equation.3  covered by the ball is given by  EMBED Equation.3  where  EMBED Equation.3 = initial velocity (ft/s)  EMBED Equation.3 = acceleration due to gravity ( EMBED Equation.3 )  EMBED Equation.3  = time  EMBED Equation.3  Given  EMBED Equation.3   EMBED Equation.3   EMBED Equation.3   EMBED Equation.3  we have  EMBED Equation.3   EMBED Equation.3  The above equation is a quadratic equation, the solution of which would give the time it would take the ball to reach the ground. The solution of the quadratic equation is  EMBED Equation.3  Since  EMBED Equation.3  the valid value of time  EMBED Equation.3  is  EMBED Equation.3 . NONLINEAR EQUATIONSTopicSolution of quadratic equationsSummaryTextbook notes on solving quadratic equationsMajorGeneral EngineeringAuthorsAutar KawDate DATE \@ "MMMM d, yyyy" \* MERGEFORMAT July 3, 2009Web Site HYPERLINK "http://numericalmethods.eng.usf.edu" http://numericalmethods.eng.usf.edu     03.01. 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